Incremental relaying for the Gaussian interference channel with a degraded broadcasting relay

This paper studies a two-user Gaussian interference channel with an in-band-reception and out-of-band-transmission relay, where the link between the relay and the two receivers is modeled as a degraded broadcast channel. It is shown that a generalized hash-and-forward (GHF) relaying strategy can achieve the capacity region of this channel to within a constant number of bits in a certain weak relay regime, where the transmitter-to-relay link gains are not unboundedly stronger than the interference links between the transmitters and the receivers. In such a regime, the GHF relaying strategy can be performed in an incremental fashion, where the relay message to one receiver is a degraded version of the message to the other receiver. A generalized-degree-of-freedom analysis reveals that in the symmetric channel setting, each common relay bit can improve the sum rate roughly by about one bit or two bits asymptotically, and the rate gain can be thought as coming solely from the improvement of the common message rates.